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Computationally Efficient Nonlinear Chebyshev Models Using Common-Pole Parallel Filters with the Application to Loudspeaker Modeling

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Many audio systems show some form of nonlinear behavior that has to be taken into account in modeling. For this, often a black-box model is identified, coming from the generality and simplicity of the approach. One such model is the polynomial Hammerstein model, which uses parallel branches that have a polynomial-type nonlinearity and a linear filter in series. For example, Chebyshev models use Chebyshev polynomials as nonlinear functions, making model identification a very straightforward procedure by logarithmic swept-sine measurements. This paper proposes a highly efficient implementation of Chebyshev models by using fixed-pole parallel filters for the linear filtering part. The efficiency comes both from using common-pole modeling and from applying a warped filter design that takes into account the frequency resolution of hearing. Due to its efficiency, the proposed model is particularly well suited for the real-time digital simulation of weakly nonlinear devices, such as amplifiers, nonlinear effects, or tube guitar amplifiers.

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